Segment 3 is the part from FS550 to the Wilderness boundary at Wellington Lake. What you are considering is linking segments 1, 2 and 3. Waterton to the South Platte River is segment 1 and segment 2 is the river up through the Buffalo Creek burn (this is not the Hayman scar, that's farther to the south near Kelsey and Deckers) to Little Scraggy TH.
I've done this section several times over the years, as a complete knob with a huge backpack, then overloaded with a trailer and now with bags. When we still lived in Denver I would start at home (we lived close to the South Platte greenway near Broadway and Evans) and do it as an out-and-back over a weekend. It's roughly 28 miles from the Waterton parking lot the Little Scraggy parking lot at CO126. Then within the Buff Creek area it's technically about 12 miles from the parking lot to the boundary on the CT. From my house to Wellington Lake and back was almost exactly a century.
You've probably done the flat spin up Waterton, a few miles of warm up. Stop at the dam to eat and shed a layer. Start up the climb, bear right at the caretaker's house, left points you towards Indian Creek. You'd eventually loop around but you have plenty of miles ahead no need to do additional. When you top out at Lenny's Rest, which is a bench honoring Leonard Southwell, a deceased Eagle Scout, go right. Left is the other side of the Indian Creek and Roxborough Loop. The trail then climbs for a few miles through a couple of drainages (Bear Creek) before finally descending to the river for a couple of miles. If we were starting after work on a Friday (from the Waterton parking lot in that case) we'd camp somewhere between Lenny's and the descent, there are lots of opportunities.
Segment 2 is pretty sparse, still not much shade and no opportunity for water. Fill up at the South Platte if there is any question. The next chance for water isn't until Buffalo Creek. Before the fire (which was 1996) there were all kinds of 4x4 and motorcycle trails up here and a nice campground called Top of the World. There are a couple of trailheads still but it's a lot less busy now than back then. You climb for a few miles from the river, past a couple of old mines (they are getting hard to spot), but it's not super steep and the last few miles is mostly flat. It's really pretty up there especially in the spring when the flowers are growing but by mid summer it gets really hot and dry. I would not plan on camping personally.
For segment 3 when you cross over highway 126 you'll be close to the main recreation area parking lot. If you want to stay on the CT go up onto Green Mountain to camp, this is located between the Buffalo CG and Meadows group campground, or all the way out to the end on Rolling Creek. These are going to be a lot more peaceful than camping along the CT itself. I don't get too hung up riding on the trade route because there are so many more fun trails we've built in Buffalo Creek. But for touring the CT is probably best, more options to fill up your water and not much technical.
Segment 1 with a trailer takes me about 4~5 hours of cycling, segments 2 & 3 each about 2.5~3 hours. The whole thing out and back to Waterton can be done in a day if you really get after it (I've been able to almost do it just once, I usually hit my turn around time at the end of segment 2 though) and if you go lighter with your gear you can shave a lot of time on segment 1 (the 7ish miles between the dam and the start of the South Platte descent get to be a drag with a trailer) and make it a quick overnight. But we always end up with a couple of beers, a little flask, some real food and make it a weekend and stop too much. We're not competitive ultra endurance racers or anything so we tend to bring creature comforts to relax with, like a book and maybe mess with a little ham radio.